What is the driving force behind the weather on earth?

The SUN. !!!!

Not only does it give daylight and rotate about it under gravity, but its radiation drives the weather , by heating or cooling. Thereby giving us rain/precipitation or dryness, calm of blowing winds. The connection is very tenuous and indirect, but with out the Sun , these weather phenomina would not occur.

NB THe SUN drives everything in the Solar system.